Answer is $4$. The relations are as shown:
$\langle a_{11}, a_{12}\rangle$ for $E_1$
$\langle a_{21}, a_{22}\rangle$ for $E_2$
$\langle a_{31}, a_{32}, a_{11}\rangle$ for $E_3$ and $E_1-E_3$ relationship
$\langle a_{11}, a_{21}\rangle$ for $m:n$ relationship $E_1-E_2$
We cannot combine any relation here as it will give rise to partial functional dependency and thus violate $\text{3NF}.$
Reference: MIT notes